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'APER FOLDING AND CUTTING 



A SERIES OF 



FOLDINGS AND CUTTINGS 



ESPECIALLY ADAPTED TO 



KINDERGARTENS AND PUBLIC SCHOOLS 



BY 



KATHERIXE M. BALL 




AFh 28 1893 



BOSTON 
THE PRANG EDUCATIONAL COMPANY 



ef \j^ASHm: 



&&> 



^/072.-^ 






Copyright, 1892, by 
THE PRANG EDUCATIONAL COMPANY. 



AUTHOR'S PREFACE. 



-o-u^«4c 



I ^VERY scheme for art education must necessarily embrace 
^-^ the study of geometric plane figures and their mechan- 
ical construction. 

The prescribed methods for this construction have been 
lifficult, complicated, consuming much time, and, if learned at 
l11, were easily forgotten. 

Children would easily follow a dictation which would result 
n an octagon, hexagon, pentagon, etc., but were unable to- 
epeat it independently the following day. 

After various unsuccessful attempts to simplify the method 
)f drawing these figures, my attention was called to paper 
olding and cutting. 

The ease and interest with which the children would make 
he four-pointed star, the four-leaved rosette, and the equi- 
ateral triangle, as outlined by The Prang Course of Drawing, 
uggested that possibly other figures, such as the crosses, the 
refoil, the quatrefoil, the octagon, the hexagon, and pentagon, 
night be made in a similar manner. 

3 



4 AUTHOR'S PREFACE. 

After much thought and study, I discovered the principle 
underlying such construction of all regular plane geometric 
figures. It is simple, and within the comprehension of very 
young children. 

It is a great help in teaching simple design, inasmuch as 
the children make their figures from paper instead of drawing 
them, thus dealing with the concrete rather than the abstract 
thing, and by so doing they get broad, simple effects, instead 
of the confusing and meaningless arrangement of lines called 
designs. Inasmuch as it consumes very little time, the child 
can make a second or third trial in the same lesson, correcting 
the unsatisfactory parts, thus enabling them to make three 
figures where before they made one. 

Again, these exercises will be found to be valuable in 
making patterns for the designs in colored papers, which are 
now taking the place of the decorative drawing in the drawing- 
books. 

I have taken great pleasure in arranging this series of 
exercises, hoping that they may be a source of help to all 
teachers interested in Art Education and Manual Training, and 
that they may give a new impetus to form study and design, 
by being associated with paper folding and cutting, w^hich is 
always a source of delight to the children. 

KATHERINE M. BALL. 



LIBRARY OF CONGRESS - BINDING RECORD 
Call No. LB1187.B21 Date3-lW9 



Author 
Title 



Date Block & Item 

Reblad style Mb« 

Specs. ■■ 



7-56 (rev V72) 



Vol. Copy No. of vols.- 

D161-79-220 




CONTENTS. 



PAGE 

The Principles underlying the Work 7 

CHAPTER I. 
General Suggestions 9 

CHAPTER n. 
Method of Presentation , .11 

CHAPTER HI. 
Evolution of Units and their Application in Design . . 17 

CHAPTER IV. 
Foldings and Cuttings from the Square and Circle: 

Circle, Square, Four-pointed Star, Quatrefoil, Crosses, and Rosettes 22 

CHAPTER V. 
Foldings and Cuttings from the Square and Circle : 

Equilateral Triangle, Three-pointed Star, Trefoil, and Three-leaved 
Rosettes, Hexagon, Six-pointed Star, Hexafoil, and Six-Leaved 
Rosettes 27 

5 



6 CONTENTS. 

CHAPTER VI. 

PAGE 

Foldings and Cuttings from the Square and Circle: 

Pentagon, Five-pointed Star, Cinquefoil, and Five-leaved Rosettes 33 

CHAPTER Vn. 
Foldings and Cuttings from the Square and Circle : 

Heptagon Seven-pointed Star, Heptafoil, and Seven-leaved Rosettes 37 

CHAPTER Vni. 
Foldings and Cuttings from the Square and Circle: 

Nonagon, Nine-pointed Star, Nonafoil, and Nine-leaved Rosettes . 40 

CHAPTER IX. 
Borders 43 



PAPER FOLDING AND CUTTING. 



D>^C 



A simple method of snaking I'egular plane geometric figures fro?n a square, 
a circle^ or any regular or irregular geometric plane figure, by nieans of 
folding in such a ma7iner that one clip of the scissors will give the 
desired result. 



PRINCIPLES UNDERLYING THE WORK. 

'T"^HE principle upon which this folding is made is the 
-■- division of the 360° of the circle, or imaginary circle, 
contained within the enclosing plane figure into as many parts 
as there are sides or angles to the figure. 

The paper may be square, circular, or of any regular or 
irregular shape. 

We fold it into two equal parts, as in the circle (or as near 
equal as can be obtained in the other figure); this gives the 
180° fold. 

By bisecting and folding, we get the 90° fold. 

By dividing the 180° fold into two and a half parts, and 
folding, we get the 72° fold. 

7 



8 PAPER FOLDING AND CUTTING. 

By trisecting the i8o° fold, and folding, we get the 60° fold. 

By dividing the 180° fold into three and a half parts, and 
folding, we get the 5i|° fold. 

By bisecting the 90° fold, and folding, we get the 45° fold. 

By dividing the 180° fold into four and a half parts, and 
folding, we get the 40° fold. 

By cutting each of these folds so that the result will be an 
isosceles triangle, we get from the 90° fold the square ; from 
the 72° fold, Wi^ pentagon; from the 60° fold, the Jicxagon ; 
from the 5if° fold, the Jieptagon ; from the 45° fold, the octagon; 
and from the 40° fold, the nonagon. 

For the equilateral triangle it is necessary to cut the 60° 
fold so that the result will be a right-angled triangle. 

The accuracy of the result of this construction will naturally 
depend upon the accuracy of the folding and cutting. 




CHAPTER I. 

GENERAL SUGGESTIONS. 

THESE folding and cutting exercises were prepared in 
order to give the children a short cut to making designs 
in colored papers. 

It is not the intention to fold and cut the colored papers, 
but to make a pattern from white paper by this process, the 
pattern to be placed on the back of the colored paper and 
drawn around. By cutting on this drawn line we get the 
design. 

CUTTING. 

Teach the children to hold the scissors easily and comfort- 
ably. In cutting long lines, the scissors should be opened widely, 
so that the entire length may be cut at one time. In cutting 
curved lines, the scissors and paper should approach each other 
equally, both describing the curve. In cutting around small 
curves into small places, it will be found necessary to use the 
points of the scissors with very short cuts. 

PASTING. 

Apply to the terminal points of the design, with a tooth- 
pick, small pieces of paper, or brush, the smallest possible 

9 



10 PAPER FOLDING AND CUTTING. 

amount of paste. Lay a blotter or piece of paper on the 
design, and rub quite hard on the pasted places without moving 
the overlying paper. Place the result under some weight which 
will be sufficient to press it evenly until dry, 

ROSETTES. 

In all rosettes, arrangements having repeats radiating from 
a centre, arrangements which are not figures complete in them- 
selves, a centre-piece should be applied. It should be the same 
color as the units, and generally occupy about a third of the 
width of the design. 



For further information concerning color, making arrange- 
ments, etc., refer to the Prang color manual, called '* Color 
Instruction : Suggestions for a Course of Instruction in Color 
for Public Schools. 




CHAPTER II. 

METHOD OF PRESENTATION. 

THIS work is intended to follow the simple outline for 
folding found in "The Prang Primary Manual," therefore 
it is unnecessary to go into detail as to preliminary exercises. 

The children, having learned to fold edge to edge and 
corner to corner, having bisected, trisected, and quadrisected 
paper by folding, are now ready to take up the construction of 
geometric figures, stars, rosettes, and borders. 

The method of presentation embraces dictation, imitation, 
and imagination. 





Fig. I 



F.G.2 




Fig. 3 




F.G 4 



With the square in the hands of the children, they bisect it 
by folding 1-2 on 3-4, as in Fig. i, obtaining Fig. 2. Again 
they bisect Fig. 2 by folding 1-2 on 3-4, obtaining Fig. 3. 



II 



12 



PAPER F0LD4NG AND CUTTING. 




Holding Fig. 3 by the closed corner (which is the centre 

of the original square) in the left hand, ask the children what 

kind of a figure they would get by cut- 
ting a curved line, concave to the centre 
of the square or curving outward, con- 
necting points I and 2. 

After they have worked upon their 
imagination for the result, let them make 
the trial, comparing results. 
Next ask them to tell you what kind of a figure they would 

get by connecting 1-2 with a curved line curving inward. 

They may not be able to describe it in words, but may make a 

simple drawing on their slates or paper. Have them make the 

cut and again compare results. They may then in like manner 

connect i and 2 with a straight line. 

They may now fold to Fig. 4, page 11. By folding to Fig. 3 

and then folding i on 2, they 

will get Fig. 4. Reversing it 

and holding the fold at the 

original square's centre, o, 





what will they get by cutting 
a straight line from i to 2, as 
a ? or a curved line, as d ? 
Both exercises may be cut. 

Now ask the children how many can fold and cut a figure 
from a drawing on the board. Draw the quatrefoil c, page 13, 
on the board, and let the children make the trial. 



METHOD OF PRESENTATION. 



13 




Those who fail may be assisted in this manner : Give them 
a fresh square and ask them to draw the quatrefoil upon it; 
then fold to Fig. 4, keeping the drawn lines 
on top. 
V . / Ask the children what the repeating unit 

^ ^\^ is. (A circle.) Ask how much of the re- 

peating unit can be seen on the fold. (Half.) 
By cutting on the drawn line, they will get 
^ the figure. 

If the fold is not held at the closed corner, o, when cutting, 
the children may be much surprised to find they have a num- 
ber of small, meaningless 
pieces of paper instead 
of a completed figure. 
A little experience will 
soon correct this. 

Figures like those at 
the right may be put on 
the board, which the chil- 
dren may make. 

Frequently the chil- 
dren will get a fair imi- 
tation of the drawing, 
yet their proportion of 
parts may be such as to 

make an undesirable result. Then it will be necessary to lead 
them to analyze the drawing, to enable them to more closely 






14 



PAPER FOLDING AND CUTTING. 



observe it. For instance, in the quatrefoil, ask, What kind of 
curves are to be found ? Where does the curve begin and 
where does it end ? At what point on the diameter do the 
curves meet, and what kind of an angle do they make ? How 
near the corner of the square does the curve come ? etc. 

After a series of such questions, have the children make a 
second or a third trial, until they get something which is satis- 
factory. 

The folding and cutting do not consume much time ; for this 
reason it will be found that the children can accomplish more 
by cutting than by drawing in the given time. , 



FIGURES HAVING THREE OR SIX PARTS. 

In taking up figures having three or six parts, we must show 
the children that, in order to get three or six parts, the whole 
square must first be divided into three or six parts. 




Tio. I 



Fig. 2 



Thus far the children have divided the paper by bisecting 
or trisecting the sides and connecting points of division, as 
I. Now we want a division which is made by lines radi- 



Fig 



!i i 



METHOD OF PRESENTATION. 



15 



ating from the centre, as Fig. 2. In Fig. i, we divide the space 
into parts having equal size and shape ; in Fig. 2, we divide 
the space so that the angles at the centre of the square will 
be equal. 

It is a very easy matter to make a division having eight 
equal angles, as all it requires is to fold diameters and diago- 
nals ; but one having three or six is much more difficult. 

As six embraces three, we will take six first. Ask the chil- 
dren to make a trial, first placing a point in the centre of the 
square, and drawing the division lines radiating from it, as a. 

Have them test the accuracy by folding i on 2, and then 
into thirds, to see if the parts are equal. 





a o 

If it is found that the division of the square is too difficult, 
try the circle, as b, in a similar manner. Inasmuch as the 
radiating lines will be of the same length, it may be better 
understood. 

It will now be an easy matter to lead them to the folds 
as given for all three and six leaved rosettes. 



16 



PAPER FOLDING AND CUTTING. 



FIGURES HAVING FIVE PARTS. 





For figures having five parts, the square must be divided 
into five parts, the dividing lines radiating from the centre and 
making the five central angles the same, as c. 

If the children cannot comprehend this, have thqm use a 
circle, as d, and it may be simpler. Then try the division of 

the square afterwards. 

If the whole square is divided into 

five parts, the half square must be 

divided into two parts and a half, as c. 

It will now be an easy matter, fold- 

e ing from o, to fold i on 2, and the 

remaining half part underneath, thus giving us the fold for 

five-leaved rosettes. 




CHAPTER III. 

THE EVOLUTION OF UNITS AND THEIR APPLICATION 

IN DESIGN. 

THE general proportion and the simple and shapely outline 
of the kite make it the type for many figures used as 
repeats in design ; any slight modification of its outline will 
produce a new figure, as shown in these illustrations : — 





17 



IS 



PAPER FOLDING AND CUTTING. 












In the kite, and the units based on it,^ we find the greatest 
width above the centre. 



1 This " Evolution of Units " is taken from " The Prang Course in Drawing." 



THE EVOLUTION OF UNITS. 



19 



There are other pleasing historic repeats, in which the 
greatest width is below the centre. Examples of the kind 
are given in these illustrations : — 













The upper and lower rows are Moorish ; the middle row is 
Gothic. 



20 



PAPER FOLDING AND CUTTING 




a 



In exercises in invention, have the child modify the kite, 
making his own unit and applying it to the different geometric 
figures. While the same unit may be used for all the designs, 
its adaptation to the spaces of the different figures must neces- 
sarily change its proportions, making it wider, as in the square, 
and very much narrower, as in the octagon. 

Inferring that the child has modified 
the kite into this unit, a, he may fold the 
square, from which the design is to be cut, 
to Fig. 4 of Cliapter II., and draw on it 
half of the unit, as b. If he should cut 
from o through i to 3, his result would be 
four separate pieces, as there would be noth- 
ing to hold it together at the centre ; but, 
by cutting from i to 2, point 2 being the 
tangential union of the lines 2-1 and 0-3, 
the design will be complete, as c. 

He will now be interested to see the 
effect of the repetition of this unit in the ^ 

octagon, the triangle, the hexagon, and the pentagon, as illus- 
trated in Figs. I, 2, 3, 4, page 19. 

For the octagon, he must fold to Fig. 5 of Chapter IV. ; 
for the triangle, to Fig. 4 of Chapter V. ; for the hexagon, 
to Fig. 5 of Chapter V. ; and for the pentagon, to Fig. 5 of 
Chapter VI. ; always making the drawing of the half unit 
comfortably fill the space on the fold. 

Should the child use for his design a unit that in itself 




THE EVOLUTION OF UNITS. 



21 





Fig. I. 



Fig. 2. 





Fig. 3. F'g- 4. 

would not make a centre, he would have to provide for this in 
his drawing on the fold. For instance, in selection a, which is 
the kite, should he cut on the en- 
tire outline, his design would fall 
apart; but by drawing a centre 
on it, as in i-2 in b, and cutting 
from 3 to 2 and 2 to i, as in r, 
he will then have a centre which 
holds the units together, and his design will be complete. 




CHAPTER IV. 



FOLDINGS AND CUTTINGS FROM THE SQUARE 

AND CIRCLE. 

TO make, by folding and cutting, a square, a circle, a 
regular octagon, a four-pointed star, an eight-pointed 
star, a quatrefoil, an octafoil, a four-leaved rosette, an eight- 
leaved rosette, from a square, circle, or any regular or irregular 
plane figure. 









THE SQUARE. 








2 






/"\ 


v 


/' 


\ 






360° 




A 


V 

90° 


22i\ 


45' 







Tic> I / ' Fig 2 Fig 3 Fig.5 FiG4 

For Figs. 2, 3, and 4, fold i on 2, and crease with the 




thumb-nail. For Fig. 5, bisect 
the angle at o in Fig. 4, and fold. 



THE CIRCLE. 



Fold to Fig. 4, and cut from 
I to 2. Points I and 2 are equally 
distant from o. 



22 



FOLDINGS AND CUTTINGS FROM THE SQUARE. 



23 



THE SQUARE. 

Fold to Fig. 4, and cut from 
I to 2. Point 2 is a bisection of 
3-0. 




THE REGULAR OCTAGON. 

Fold to Fig. 4, and cut from 
I to 2. Points I and 2 are equally 
distant from o. 




THE FOUR-POINTED STAR. 

Fold to Fig. 4, and cut from 
I to 2. Point I is a bisection of 
3-0. 




THE EIGHT-POINTED STAR. 

Fold to Fig. 5, and cut from 
I to 2. Point 2 is nearer to 3 
than to o. 




24 



PAPER FOLDING AND CUTTING. 





THE QUATREFOIL. 

Fold to Fig. 4, and draw on 
the fold a semicircle, and cut from 
I to 2. Point I is the tangential 
union of the semicircle and the 
line 3-4. 

THE OCTAFOIL. 

Fold to Fig. 5, and draw on 
the fold a semicircle, and cut from 
I to 2. Point 2 is the tangential 
union of the semicircle and the 
line 3-0. 



FOUR-LEAVED ROSETTES. 
Fold to Fig. 4, and cut from i to 2. 





FOLDINGS AND CUTTINGS FROM THE CIRCLE. 



25 




N 









THE CIRCLE. 
Fold I on 2, and crease with the thumb-nail. 





Tig I 



Fig 2 



F.G 3 



^0 0' 

46° 22'^' 



Fig 4 F(G,5 



For the square, fold to Fig. 3, and cut from i to 2. 2 
For the octagon, fold to Fig. 4, and cut from i to 2. 
For the four-pointed star, fold to Fig. 4, and cut 3 
from I to 3. Point 3 is obtained by trisecting 2-0. 




26 



PAPER FOLDING AND CUTTING. 



QUATREFOILS. 

Fold to Fig. 4, and cut from i to 2. 





EIGHT-LEAVED ROSETTES. 
Fold to Fig. 5, and cut from i to 2. 





CHAPTER V. 



FOLDINGS AND CUTTINGS FROM THE SQUARE 
AND CIRCLE. —Continued. 

TO make, by folding and cutting, an equilateral triangle, 
a hexagon, a three-pointed star, a six-pointed star, a 
trefoil, a hexafoil, a three-leaved rosette, and a six-leaved 
rosette, from a square, a circle, or any regular or irregular 

plane figure. 

THE SQUARE. 





Fio 2 



Fig. 4 



Fio. I 




Fig. 3 



Beginning with the square, Fig. i, fold i on 2, folding from 
o, and crease with the thumb-nail, thus obtaining Fig. 2. 

To obtain Fig. 3, trisect the 180° fold in Fig. 2, and fold the 
right part on the adjoining one, folding from o. For Fig. 4, 

27 



28 



PAPER FOLDING AND CUTTING. 



fold the remaining part, seen in Fig. 3, on top of the first fold, 
and crease. For Fig. 5, bisect and fold Fig. 4. 



THE EQUILATERAL ' 

TRIANGLE. | 

Fold to Fig. 4, and cut ^ 

from I to 2. The line 1-2 j 

must be at right angles to j 

3-0. ^ 




THE REGULAR HEXAGON. \ 

Fold to Fig. 4, and cut i 
from I to 2. Points i and 

2 must be equally distant j 

from o. j 



i 

THE THREE-POINTED STAR. i 

Fold to Fig. 4, and cut j 
from I to 2. Point 2 is ob- 1 
tained by quadrisecting 3-0. 1 



FOLDINGS AND CUTTINGS FROM THE SQUARE. 



29 



THE SIX-POINTED STAR. 

Fold to Fig. 5, and cut 
from I to 2. Point 2 is ob- 
tained by trisecting 3-0. 




THE TREFOIL. 

Fold to Fig. 4, and cut 
from I to 2. Point 2 is the 
intersection of the line 3-0 
and the arc. The arc should 
be a semicircle, having its 
centre on the line i-o. 




THE TREFOIL. 

Fold to Fig. 4, and cut 
from I to 2. The arc 4-1 
should be a quadrant, with 3 
as centre. The line 2-4-1 
must be at right angles with 
5-0. 




30 



PAPER FOLDING AND CUTTING. 




THE HEXAFOIL. 

Fold to Fig. 5, and cut 
from I to 2. Point 2 is the 
tangential union of the arc 
and the line 3-0. The arc 
should be a semicircle, hav- 
ing its centre on the line i-o. 



THE HEXAFOIL. 

Fold to Fig. 5, and cut 
from I to 2. The line 2-4 
must be at right angles to 
i-O, and the arc 3-1 should 
be a quadrant with 4 as cen- 
tre. 



THREE-LEAVED ROSETTES. 
Fold to Fig. 3, and cut from i to 2. 




FOLDINGS AND CUTTINGS FROM THE CIRCLE. 



31 




THE CIRCLE. 




Fig J 



For the triangle, fold to Fig. 3, and cut from i to 2. 
For the hexagon, fold to Fig. 4, and cut from i to 2. 
For the six-pointed star, fold to Fig 5, and cut from 
I to 2. Point 2 is obtained by trisecting 3-0. 



3 I 



.32 



PAPER FOLDING AND CUTTING. 



SIX-LEAVED ROSETTES. 

Fold to Fig. 5, and cut from i to 2. 







CHAPTER VI. 

FOLDINGS AND CUTTINGS FROM THE SQUARE 
AND CIRCLE. — Continued. 

TO make, by folding and cutting, a regular pentagon, a 
five-pointed star, a cinquefoil, and a five-leaved rosette, 
from a square, a circle, or any regular or irregular plane figure. 

THE SQUARE. 




Fig I 



Beginning with the square. Fig. i, fold i on 2, and crease 
with the thumb-nail, thus obtaining Fig. 2. 



34 



PAPER FOLDING AND CUTTING. 



To obtain Fig. 3, divide the 180° fold into two and a half 
parts, and fold the right part on to the adjoining one, folding 
from o in Fig. 2. For Fig. 4, reverse the position of the fold, 
making the rear face the front face, and fold the remaining half 
part, seen in Fig. 3, over the other fold. For Fig. 5, bisect 
Fig. 4, folding the left half under the right half. 




THE REGULAR PENTAGON. 

Fold to Fig. 4, reverse the 
position of the fold, and cut 
from I to 2. Points i and 
2 must be equally distant 
from o. 




THE FIVE-POINTED STAR. 

Fold to Fig. 5, and cut 
from I to 2. Point 2 is 
nearer to o than to 3. 



FOLDINGS AND CUTTINGS FROM THE S 



9/ 



RE. 



35 



THE CINQUEFOIL. 

Fold to Fig. 5, and cut^rom 
I to 2. Point 2 is. the tan- 
gential union of the semicircle 
and the line 4-0. The arc 
3-2-1 is a semicircle with its 
centre on the line i-o. 




THE CINQUEFOIL. 

Fold to Fig. 5, and cut from 
I to 2. The arc 4-1 should be 
a quadrant with 3 as centre, 
and the line 2-4-3 should be 
at right angles with the line 
i-o. 




THE CINQUEFOIL. 

Fold to Fig. 5, and cut from 
I to 2. The arc 2-1 should be 
a quadrant with 3 as centre. 




36 



PAPER FOLDING AND CUTTING. 



THE CIRCLE. 




Tig. I 



Fig. 2 



F.0.3 




72 o 




36 *» 


hCrA 


T\o.5 



FIVE-LEAVED ROSETTES. 

Fold to Fig. 5, and cut from i to 2. 





CHAPTER VII. 

FOLDINGS AND CUTTINGS FROM THE SQUARE 
AND CIRCLE. — Continued. 

TO make, by folding and cutting, a heptagon, a seven- 
pointed star, a heptafoil, and a seven-leaved rosette, from 
a square, circle, or any regular or irregular plane figure. 

THE SQUARE. 




Fic. I 



Beginning with the square, Fig. i, fold i on 2, and crease 
with the thumb-nail, thus obtaining Fig. 2. 

Z7 



38 



PAPER FOLDING AND CUTTING. 



To obtain Fig. 3, divide the 180° fold into two and a third 
parts, and fold the right part on the adjoining one, folding from 
o in Fig. 2. For Fig. 4, reverse the position of the fold, 
placing the rear face in front, and fold the remaining third part 
over the other fold. For Fig. 5, fold the edge i to adjoin the 
edge 2 in Fig. 4, making i-o and 2-0 meet. For Fig. 6, bisect 
the fold of Fig. 5, folding the left half under the right half. 




THE HEPTAGON. 

Fold to Fig. 5, and cut from 
I to 2. Points I and 2 are 
equally distant from o. 




THE SEVEN-POINTED STAR. 

Fold to Fig. 6, and cut from 
I to 2. Point 2 is nearer to 4 
than to 3. 



FOLDINGS AND CUTTINGsifROM THE SQUARE. 



39 



THE HEPTAFOIL. 

Fold to Fig. 6, and cut from 
I to 2. Point 2 is the tangen- 
tial union of the semicircle and 
the line 3-0. The semicircle 
must have its centre on the 
line i-o. 




THE SEVEN-LEAVED ROSETTE. 

Fold to Fig. 5, and cut from 
I to 2. 




. CHAPTER VIII. 

FOLDINGS AND CUTTINGS FROM THE SQUARE 
AND CIRCLE. — Concluded. 

TO make, by cutting and folding, a regular nonagon, a 
nine-pointed star, a nonafoil, and a nine-leaved rosette, 
from a square, circle, or any regular or irregular plane figure. 

THE SQUARE. 




Fig I 



f.<>3 



FiG 5 Tig 6 



Beginning with the square, fold i on 2, and crease with the 
thumb-nail. 

40 



FOLDINGS AND CUTTINGS FROM THE SQUARE. 



41 



To obtain Fig. 3, divide the 180° fold into two and a fourth 
parts, and fold the right part on the adjoining one, folding 
from o in Fig. 2. For Fig. 4, reverse the position of the fold, 
making the back face, the front face, and fold the remaining 
fourth part over the other fold. For Fig. 5, bisect Fig. 4 by 
folding I on 2, placing the left half under the right half. For 
Fig 6, bisect Fig. 5 by again folding i on 2, and placing the 
left half under the right half. 



THE REGULAR NONAGON. 

Fold to Fig. 5, and cut from 
I to 2. Points I and 2 are equally 
distant from o. 




THE NINE-POINTED STAR, 

Fold to Fig. 6, and cut from 
I to 2. Point 2 is nearer to o 
than to 3. 




42 



PAPER FOLDING AND CUTTING. 




THE NONAFOIL. 

Fold to Fig. 6, and cut from 
I to 2. The arc 1-2 is a quad- 
rant with 3 as centre. 




THE NINE-LEAVED ROSETTE. 

Fold to Fig. 6, and cut from 
I to 2. 



CHAPTER IX. 



BORDERS. 



A BORDER WHICH HAS AN UPWARD GROWTH. 

CUT an oblong the size required for your border. Upon it 
draw marginal bands and a repeating unit, as in Fig. i. 
To obtain Fig. 2, fold the paper into as many parts as the 



12 



FiGr. I 



rio.2 



A? 



Fig. 3 




F10.4 



Fig-. 5 



oblong 1-2-3-4 will be contained in it. For Fig. 3, bisect 
Fig. 2 by folding. For Fig. 4, cut from i to 2 for the upper 
marginal strip, and from 3 to 4 for the unit and connecting 

43 



44 



PAPER FOLDING AND CUTTING. 



lower marginal strip. For Fig. 5, mount the border and mar- 
ginal strip, giving them the same relation as in Fig. i. 

OTHER BORDERS. 




FiG. I 





FiG 2 



FiG. 3 




BORDERS, 



45 




Fig. I 





Fig. 2 



Fig. 3 




PAPER FOLDING AND CUTTING 



A SERIES OF 



FOLDINGS AND CUTTINGS 



ESPECIALLY ADAPTED TO 



KINDERGARTENS AND PUBLIC SCHOOLS 



BY 



KATHERINE M. BALL 




BOSTON 
THE PRANG EDUCATIONAL COMPANY 



RD-16.1 





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